"Last time we got this far was in 1911 – my great-grandad's day," says Muhammad Abdur Raqeeb, cracking his face open into a broad grin. "Mind you, he didn't know much about the FA Cup. He was farming in Sylhet – in modern-day Bangladesh – at the time."

Things are very different now for 35-year-old Raqeeb's family. "Bradford born and Bradford through-and-through," he says, at the Bangladesh Youth Organisation two streets from Bradford City's ground at Valley Parade where claret-and-amber jubilation reigns amid piles of shovelled snow.

"Everyone's dead chuffed," he says, echoed by his colleague Zulfiqar Ali, who had a boisterous morning discussing the Bantams' 4-3 walloping of Premier League Aston Villa – to reach the Capital One Cup final at Wembley next month – with a group of school-excluded teenagers who attend classes at the centre instead.

More of a cricketing man, who played for Bradford Moor in the city's Quaid-e-Azam Sunday league, 47-year-old Ali sees parallels between the two games. "Some of the lads here support Man U or Liverpool or other big clubs, but if they're from Bradford, they come back to City in the end, and they're certainly with them now," he says. In the same way, his league's title – commemorating Muhammad Jinnah the founder of Pakistan – uses sport to cement community pride.

The group's homely warren of rooms is close to the garage where you used to be able to find star player George Robinson working as a mechanic – a veteran not just of the 1911 Cup final but of City's first fixture, against Grimsby in 1903.

A mile away, in the grandeur of Victorian city hall, Bradford's first citizen is bursting with satisfaction. Lord mayor Dale Smith, says: "I'm over the moon. I watched the match on the television with my wife. It's a real tonic for the city and I can tell you, whichever team we are up against in the final, they'll have a job to overcome us."Smith is a Conservative councillor in Wharfedale ward, part of a rural fringe which usually frets at being linked with Bradford and looks longingly at nearer and more affluent North Yorkshire. The fact that the "City effect" has taken root here is reckoned particularly significant by Colin Philpott, chief executive of Bradford Breakthrough's boostering partnership of local business, government agencies and Bradford University.

"The feeling's even spread to Ilkley," says Philpott, who retired last year as head of Bradford's biggest attraction, the National Media Museum, which uses every means possible to woo visitors nervous about the city's glum image among outsiders.

"This is more than feelgood; a positive story, and one that's developed as the cup run has gone on, really does have the potential to give us what we need – investment and visitors from other parts of the country."

Mike Cartwright of Bradford chamber of commerce picks up on the link between image and economic well-being, drawing parallels with Yorkshire's triumph in landing the start of the Tour de France in 2014. He says: "It's difficult to put a figure on it in cash terms, like the £100m they're talking about from the Tour, but we've already seen a rise in visitor numbers and that's going to continue between now and the cup final on 24 February."Dr Mohammad Ali of Bradford's QED agency, which supports ethnic minority businesses, was joined for the semi-final second leg by 30 of the visitors – a group of leading young military personnel and civil servants from overseas, hosted by the government's Defence Academy.

He says: "We're seeing a revival in Bradford at last, not just visitors but new businesses starting up — I'm seeing more all the time on my journey to work. Bradford City is doing a lot for that."

Cash was meanwhile clinking into the tills at the club's Bantam's shop, where two lots of three-generation City supporters were stocking up for the final. Management consultant Stuart Gracey brought along his son Ben, who works at Bradford Royal Infirmary, and grandson William, to forage for a four-year-old's strip for the big day.

In the next aisle, primary school headteacher Lindsay Lomas, 37, was sizing up a much bigger version for her Dad, a loyal fan like his father and grandfather before him, to wear as he cheers on the team with her and his grandchildren.

Lomas's school is sensitively sited in sporting terms – midway between Bradford and its rivals Huddersfield and Halifax.

"But they know where I stand," she says. "We'll be doing a lot of decorating of the classrooms in claret and amber over the next five weeks."